Lotz-Rabiger's nets of Markov operators in L-1-spaces


EMELYANOV E. , Erkursun N.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.371, no.2, pp.777-783, 2010 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 371 Issue: 2
  • Publication Date: 2010
  • Doi Number: 10.1016/j.jmaa.2010.05.060
  • Title of Journal : JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Page Numbers: pp.777-783

Abstract

The Lotz-Rabiger nets (LR-nets) introduced in Rabiger (1993) [18] under the name M-nets provide an appropriate setting for investigation various mean ergodic theorems in Banach spaces. In the present paper we prove several convergence theorems for LR-nets of Markov operators in L-1-spaces which extend Theorems 1 and 5 from Emel'yanov (2004) [8]. and Theorem 1.1 from Lasota (1983) [11]. (C) 2010 Elsevier Inc. All rights reserved.